Table of Contents

1. For Alt 2 we were asked to come up with a hypothesis to investigate using a dataset.
2. The project must be completed using the Python programming language.
3. We were required to examine the raw data in order to ascertain usability.
4. We then had to analyze said data to find:
   1. Mean Distrubution of Redshift
   2. Frequency Classes of Celestial bodies
   3. Mode Distrubution of Redshift
   4. Median Distrubution of Redshift
5. This information is to be represented in graph form.
6. How would the analysis fo this information impact decision making.

Hypothesis

What was the average redshift of celestial bodies observed during the sloan digital sky survey?

Alongside this I wondered which class of celestial body appeared most frequently in this dataset.

Additional analysis

Alongside answering these questions I chose to do further analysis of the dataset

This includes;

Pearson correlations

Spearman correlations

And using various machine learning classification methods such as;

Support Vector Classifiers

Random Forest Classifiers

This image was taken from the greater sdss dataset By ESA/Hubble, CC BY 4.0, SDSS

import numpy as np
import pandas as pd

import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as ex
import plotly.graph_objs as go
import plotly.figure_factory as ff
from plotly.subplots import make_subplots
import plotly.offline as pyo

pyo.init_notebook_mode()
sns.set_style('darkgrid')

from sklearn.preprocessing import LabelEncoder
from xgboost import XGBClassifier
from lightgbm import LGBMClassifier
from catboost import CatBoostClassifier
from sklearn.ensemble import RandomForestClassifier
from sklearn.ensemble import GradientBoostingClassifier
from sklearn.metrics import accuracy_score
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import StandardScaler
from sklearn import svm
from sklearn.metrics import confusion_matrix, classification_report
from sklearn.model_selection import train_test_split

from yellowbrick.classifier import ConfusionMatrix
from yellowbrick.classifier import ClassPredictionError
from yellowbrick.classifier import ROCAUC
from yellowbrick.style import set_palette


from imblearn.over_sampling import SMOTE
from collections import Counter

fold = StratifiedKFold(n_splits=4, shuffle = True, random_state=62)

import warnings
warnings.filterwarnings('ignore')

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Cell In[4], line 18
     16 from xgboost import XGBClassifier
     17 from lightgbm import LGBMClassifier
---> 18 from catboost import CatBoostClassifier
     19 from sklearn.ensemble import RandomForestClassifier
     20 from sklearn.ensemble import GradientBoostingClassifier

ModuleNotFoundError: No module named 'catboost'

df= pd.read_csv("../input/stellar-classification-dataset-sdss17/star_classification.csv")
df = df.drop(['obj_ID','alpha','delta','run_ID','rerun_ID','cam_col','field_ID','fiber_ID'], axis = 1)
df

	u	g	r	i	z	spec_obj_ID	class	redshift	plate	MJD
0	23.87882	22.27530	20.39501	19.16573	18.79371	6.543777e+18	GALAXY	0.634794	5812	56354
1	24.77759	22.83188	22.58444	21.16812	21.61427	1.176014e+19	GALAXY	0.779136	10445	58158
2	25.26307	22.66389	20.60976	19.34857	18.94827	5.152200e+18	GALAXY	0.644195	4576	55592
3	22.13682	23.77656	21.61162	20.50454	19.25010	1.030107e+19	GALAXY	0.932346	9149	58039
4	19.43718	17.58028	16.49747	15.97711	15.54461	6.891865e+18	GALAXY	0.116123	6121	56187
...	...	...	...	...	...	...	...	...	...	...
99995	22.16759	22.97586	21.90404	21.30548	20.73569	1.055431e+19	GALAXY	0.000000	9374	57749
99996	22.69118	22.38628	20.45003	19.75759	19.41526	8.586351e+18	GALAXY	0.404895	7626	56934
99997	21.16916	19.26997	18.20428	17.69034	17.35221	3.112008e+18	GALAXY	0.143366	2764	54535
99998	25.35039	21.63757	19.91386	19.07254	18.62482	7.601080e+18	GALAXY	0.455040	6751	56368
99999	22.62171	21.79745	20.60115	20.00959	19.28075	8.343152e+18	GALAXY	0.542944	7410	57104

100000 rows × 10 columns

df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 100000 entries, 0 to 99999
Data columns (total 10 columns):
 #   Column       Non-Null Count   Dtype  
---  ------       --------------   -----  
 0   u            100000 non-null  float64
 1   g            100000 non-null  float64
 2   r            100000 non-null  float64
 3   i            100000 non-null  float64
 4   z            100000 non-null  float64
 5   spec_obj_ID  100000 non-null  float64
 6   class        100000 non-null  object 
 7   redshift     100000 non-null  float64
 8   plate        100000 non-null  int64  
 9   MJD          100000 non-null  int64  
dtypes: float64(7), int64(2), object(1)
memory usage: 7.6+ MB

df.describe().T

	count	mean	std	min	25%	50%	75%	max
u	100000.0	2.198047e+01	3.176929e+01	-9.999000e+03	2.035235e+01	2.217914e+01	2.368744e+01	3.278139e+01
g	100000.0	2.053139e+01	3.175029e+01	-9.999000e+03	1.896523e+01	2.109983e+01	2.212377e+01	3.160224e+01
r	100000.0	1.964576e+01	1.854760e+00	9.822070e+00	1.813583e+01	2.012529e+01	2.104478e+01	2.957186e+01
i	100000.0	1.908485e+01	1.757895e+00	9.469903e+00	1.773228e+01	1.940514e+01	2.039650e+01	3.214147e+01
z	100000.0	1.866881e+01	3.172815e+01	-9.999000e+03	1.746068e+01	1.900460e+01	1.992112e+01	2.938374e+01
spec_obj_ID	100000.0	5.783882e+18	3.324016e+18	2.995191e+17	2.844138e+18	5.614883e+18	8.332144e+18	1.412694e+19
redshift	100000.0	5.766608e-01	7.307073e-01	-9.970667e-03	5.451684e-02	4.241733e-01	7.041543e-01	7.011245e+00
plate	100000.0	5.137010e+03	2.952303e+03	2.660000e+02	2.526000e+03	4.987000e+03	7.400250e+03	1.254700e+04
MJD	100000.0	5.558865e+04	1.808484e+03	5.160800e+04	5.423400e+04	5.586850e+04	5.677700e+04	5.893200e+04

What the various Redshift values are

fig = make_subplots(rows=2, cols=1)

tr1=go.Box(x=df['redshift'],name='RedShift Box Plot',boxmean=True)
tr2=go.Histogram(x=df['redshift'],name='RedShift Histogram')

fig.add_trace(tr1,row=1,col=1)
fig.add_trace(tr2,row=2,col=1)

fig.update_layout(height=700, width=1200, title_text="Distribution of RedShift")
fig.show()

fig = make_subplots(rows=2, cols=1)

tr1=go.Box(x=df['plate'],name='Plate Box Plot',boxmean=True)
tr2=go.Histogram(x=df['plate'],name='Plate Histogram')

fig.add_trace(tr1,row=1,col=1)
fig.add_trace(tr2,row=2,col=1)

fig.update_layout(height=700, width=1200, title_text="Distribution of Plate")
fig.show()

ex.pie(df,names='class',title='The Proportion Of Different Stellar Classes',hole=.33)

fig = make_subplots(rows=2, cols=1,shared_xaxes=True,subplot_titles=('Pearson Correlation',  'Spearman Correlation'))
colorscale=     [[1.0              , "rgb(165,0,38)"],
                [0.8888888888888888, "rgb(215,48,39)"],
                [0.7777777777777778, "rgb(244,109,67)"],
                [0.6666666666666666, "rgb(253,174,97)"],
                [0.5555555555555556, "rgb(254,224,144)"],
                [0.4444444444444444, "rgb(224,243,248)"],
                [0.3333333333333333, "rgb(171,217,233)"],
                [0.2222222222222222, "rgb(116,173,209)"],
                [0.1111111111111111, "rgb(69,117,180)"],
                [0.0               , "rgb(49,54,149)"]]

s_val =df.corr('pearson')
s_idx = s_val.index
s_col = s_val.columns
s_val = s_val.values
fig.add_trace(
    go.Heatmap(x=s_col,y=s_idx,z=s_val,name='pearson',showscale=False,xgap=0.7,ygap=0.7),
    row=1, col=1
)


s_val =df.corr('spearman')
s_idx = s_val.index
s_col = s_val.columns
s_val = s_val.values
fig.add_trace(
    go.Heatmap(x=s_col,y=s_idx,z=s_val,xgap=0.7,ygap=0.7),
    row=2, col=1
)
fig.update_layout(
    hoverlabel=dict(
        bgcolor="white",
        font_size=16,
        font_family="Rockwell"
    )
)
fig.update_layout(height=700, width=900, title_text="Numeric Correlations")
fig.show()

le = LabelEncoder()
df["class"] = le.fit_transform(df["class"])
df["class"] = df["class"].astype(int)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[6], line 1
----> 1 le = LabelEncoder()
      2 df["class"] = le.fit_transform(df["class"])
      3 df["class"] = df["class"].astype(int)

NameError: name 'LabelEncoder' is not defined

x = df.drop(['class'], axis = 1)
y = df.loc[:,'class'].values

sm = SMOTE(random_state=42)
x, y = sm.fit_resample(x, y)

sns.countplot(y, palette='CMRmap')
plt.title("Class ",fontsize=10)
plt.show()
# Woah this is fucking broken. Why?

scaler = StandardScaler()
scaler.fit(x)
x = scaler.transform(x)

Outliers

SVC

x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.33, random_state = 42)

svm_clf = svm.SVC(kernel='rbf', C=1, random_state=0)
svm_clf.fit(x_train,y_train)
predicted = svm_clf.predict(x_test)
score = svm_clf.score(x_test, y_test)
svm_score_ = np.mean(score)

print('Accuracy : %.3f' % (svm_score_))

Accuracy : 0.967

svm_cm = ConfusionMatrix(svm_clf, classes=['GALAXY','STAR','QSO'])

svm_cm.fit(x_train, y_train)
svm_cm.score(x_test, y_test)
svm_cm.show()

<AxesSubplot:title={'center':'SVC Confusion Matrix'}, xlabel='Predicted Class', ylabel='True Class'>

print(classification_report(y_test, predicted))

              precision    recall  f1-score   support

           0       0.95      0.95      0.95     19583
           1       0.98      0.95      0.97     19561
           2       0.97      1.00      0.98     19707

    accuracy                           0.97     58851
   macro avg       0.97      0.97      0.97     58851
weighted avg       0.97      0.97      0.97     58851

visualizer = ROCAUC(svm_clf, classes=['GALAXY','STAR','QSO'])

visualizer.fit(x_train, y_train)
visualizer.score(x_test, y_test)
visualizer.show()    

<AxesSubplot:title={'center':'ROC Curves for SVC'}, xlabel='False Positive Rate', ylabel='True Positive Rate'>

visualizer = ClassPredictionError(svm_clf, classes=['GALAXY','STAR','QSO'])

visualizer.fit(x_train, y_train)
visualizer.score(x_test, y_test)
visualizer.show()    

<AxesSubplot:title={'center':'Class Prediction Error for SVC'}, xlabel='actual class', ylabel='number of predicted class'>

Random Forest Classifier

r_forest = RandomForestClassifier()
r_forest.fit(x_train,y_train)
predicted = r_forest.predict(x_test)
score = r_forest.score(x_test, y_test)
rf_score_ = np.mean(score)

print('Accuracy : %.3f' % (rf_score_))

Accuracy : 0.983

r_forest_cm = ConfusionMatrix(r_forest, classes=['GALAXY','STAR','QSO'])

r_forest_cm.fit(x_train, y_train)
r_forest_cm.score(x_test, y_test)
r_forest_cm.show()

<AxesSubplot:title={'center':'RandomForestClassifier Confusion Matrix'}, xlabel='Predicted Class', ylabel='True Class'>

print(classification_report(y_test, predicted))

              precision    recall  f1-score   support

           0       0.97      0.98      0.97     19583
           1       0.98      0.97      0.98     19561
           2       1.00      1.00      1.00     19707

    accuracy                           0.98     58851
   macro avg       0.98      0.98      0.98     58851
weighted avg       0.98      0.98      0.98     58851

visualizer = ROCAUC(r_forest, classes=["GALAXY", "STAR", "QSO"])

visualizer.fit(x_train, y_train)       
visualizer.score(x_test, y_test)        
visualizer.show() 

<AxesSubplot:title={'center':'ROC Curves for RandomForestClassifier'}, xlabel='False Positive Rate', ylabel='True Positive Rate'>

visualizer = ClassPredictionError(r_forest, classes=["GALAXY", "STAR", "QSO"])

visualizer.fit(x_train, y_train)        
visualizer.score(x_test, y_test)        
visualizer.show()   

<AxesSubplot:title={'center':'Class Prediction Error for RandomForestClassifier'}, xlabel='actual class', ylabel='number of predicted class'>